There's only one Ethereum blockchain (if you discount the Test network). Ether is the currency used on that blockchain, and should be referred to as "ether" (lower-case "e") though I'd imagine lots of people aren't particularly strict about this.
– Richard HorrocksJul 11 '16 at 7:58

@Richard Horrocks, means everybody makes their DAOs, etc. on one database? I cannot take Etherium code (is it open source?) and make my own private blockchain on Etherium tech? People are supposed to make their not related to each other applications using same shared ether supply?
– Alexei MartianovJul 11 '16 at 8:12

OK, your question is clearer now. Yes, it's open source, and yes, you can implement your own private blockchain with its own currency. But the public blockchain uses ether. There's currently no way for the public chain to interact with private chains and their currencies.
– Richard HorrocksJul 11 '16 at 8:15

@Richard Horrocks, thank you. Then I can make blockchain and declare it public. How current 'original' public blockchain is identified on the Internet?
– Alexei MartianovJul 11 '16 at 8:19

Because that original blockchain comes from a particular 'genesis block', which is hardcoded on the ethereum client. Then, all the mainstream ethereum transaction history must reference that very first block. If you want to create another blockchain, you must start to pick another genesis block and start mining from it. However, this leads to a lesser network security, so I'm not sure why would you want to do that. But for sure you could (in fact the testnet is some sort of a parallel blockchain that currently exists).
– SergeonJul 11 '16 at 10:59